Machine-learning techniques involving monotonic recurrent neural networks

Abstract

Various aspects involve a monotonic recurrent neural network (MRNN) trained for risk assessment or other purposes. For instance, the MRNN is trained to compute a risk indicator from a predictor variable. Training the MRNN includes adjusting weights of nodes of the MRNN subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN to be a monotonic function of input predictor variables. The trained monotonic RNN can be used to generate an output risk indicator for a target entity.

What is claimed is: 
     
       1. A system comprising:
 a first computing system configured for:
 receiving, from a second computing system, a risk assessment query that identifies a target entity, 
 providing a predictor variable for the target entity to a recurrent neural network (RNN), 
 computing, with the RNN, an output risk indicator from the predictor variable, the RNN having one or more layers of nodes that are interconnected, the nodes comprising one or more hidden states having stored values based on predictor values in the predictor variable, the nodes having weights causing outputs of the RNN and input predictor variables input into the RNN to have a monotonic relationship, wherein the RNN is trained by performing training operations comprising:
 accessing training samples comprising training predictor variables and training risk indicators corresponding to the training predictor variables, 
 computing, with the RNN, an updated value of an updated hidden state of the one or more hidden states as a first activation function applied to a first function, the first function comprising one or more weight matrices, and 
 adjusting the weights of the nodes of the RNN to minimize a loss function subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN and the input predictor variables input into the RNN to have the monotonic relationship, and wherein adjusting the weights comprising adjusting weight values in the one or more weight matrices, and 
 
 transmitting the output risk indicator to the second computing system; and 
 
 the second computing system, wherein the second computing system is communicatively coupled to the first computing system and is configured for controlling, based on the output risk indicator, access by the target entity to one or more interactive computing environments. 
 
     
     
       2. The system of  claim 1 , the training operations further comprising:
 wherein the first function comprises (i) a first weight matrix multiplied by the input predictor variable and (ii) a second weight matrix multiplied by a stored value of a hidden state of the one or more hidden states, and 
 wherein adjusting the weights of the nodes of the RNN comprises:
 adjusting first weight values in the first weight matrix, wherein the first weight matrix is nonnegative, and 
 adjusting second weight values in the second weight matrix, wherein the second weight matrix is nonnegative. 
 
 
     
     
       3. The system of  claim 2 , wherein computing, with the RNN, the output risk indicator comprises computing the output risk indicator as a second activation function of the RNN applied to a second function, the second function comprising a third weight matrix multiplied by the updated value of the hidden state,
 wherein adjusting the weights of the nodes of the RNN to minimize the loss function of the RNN subject to the set of monotonicity constraints further comprises adjusting third weight values in the third weight matrix, wherein the third weight matrix is nonnegative. 
 
     
     
       4. The system of  claim 3 , wherein:
 the first activation function has a respective derivative that is always nonnegative; and 
 the second activation function has a second respective derivative that is always nonnegative. 
 
     
     
       5. The system of  claim 4 , wherein:
 the first activation function has a respective range that is strictly nonnegative; and 
 the second activation function has a second respective range that is strictly nonnegative. 
 
     
     
       6. The system of  claim 5 , wherein the RNN is a long short-term memory (LSTM) network. 
     
     
       7. A method performed by one or more processing devices comprising:
 receiving a risk assessment query that identifies a target entity; 
 providing a predictor variable for the target entity to a recurrent neural network (RNN); 
 computing, with the RNN, an output risk indicator from the predictor variable, the RNN having one or more layers of nodes that are interconnected, the nodes comprising one or more hidden states having stored values based on predictor values in the predictor variable, the nodes having weights causing outputs of the RNN and input predictor variables input into the RNN to have a monotonic relationship, wherein the RNN is trained by performing training operations comprising:
 accessing training samples comprising training predictor variables and training risk indicators corresponding to the training predictor variables, 
 computing, with the RNN, an updated value of an updated hidden state of the one or more hidden states as a first activation function applied to a first function, the first function comprising one or more weight matrices, and 
 adjusting the weights of the nodes of the RNN to minimize a loss function subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN and the input predictor variables input into the RNN to have the monotonic relationship, and wherein adjusting the weights comprising adjusting weight values in the one or more weight matrices; and 
 
 transmitting the output risk indicator for the target entity to a second computing system for controlling, based on the output risk indicator, access by the target entity to one or more interactive computing environments. 
 
     
     
       8. The method of  claim 7 , wherein the first function comprises (i) a first weight matrix multiplied by the input predictor variable and (ii) a second weight matrix multiplied by a stored value of a hidden state of the one or more hidden states,
 wherein adjusting the weights of the nodes of the RNN comprises:
 adjusting first weight values in the first weight matrix, wherein the first weight matrix is nonnegative, and 
 adjusting second weight values in the second weight matrix, wherein the second weight matrix is nonnegative. 
 
 
     
     
       9. The method of  claim 8 , wherein the training operations further comprise:
 computing, by the RNN, the output risk indicator, as a second activation function applied to a second function, the second function comprising a third weight matrix multiplied by the updated value of the hidden state, 
 wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises adjusting third weight values in the third weight matrix, wherein the third weight matrix is nonnegative. 
 
     
     
       10. The method of  claim 9 , wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises processing the training samples in mini batches to adjust the weights of the nodes. 
     
     
       11. The method of  claim 9 , wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises updating the first weight values of the first weight matrix, the second weight values of the second matrix, and the third weight values of the third matrix using an exponential function. 
     
     
       12. The method of  claim 9 , wherein:
 the first activation function has a respective derivative that is always nonnegative; and 
 the second activation function has a second respective derivative that is always nonnegative. 
 
     
     
       13. The method of  claim 12 , wherein:
 the first activation function has a respective range that is strictly nonnegative; and 
 the second activation function has a second respective range that is strictly nonnegative. 
 
     
     
       14. The method of  claim 13 , wherein the RNN is a long short-term memory (LSTM) network. 
     
     
       15. A non-transitory computer-readable medium embodying program code for making a risk assessment, the program code comprising instructions that, when executed by a processor, cause the processor to perform operations comprising:
 providing a predictor variable for a target entity identified in a risk assessment query to a recurrent neural network (RNN); 
 computing, with the RNN, an output risk indicator from the predictor variable, the RNN having one or more layers of nodes that are interconnected, the nodes comprising one or more hidden states having stored values based on predictor values in the predictor variable, the nodes having weights causing outputs of the RNN and input predictor variables input into the RNN to have a monotonic relationship, wherein the RNN is trained by performing training operations comprising:
 accessing training samples comprising training predictor variables and training risk indicators corresponding to the training predictor variables, 
 computing, with the RNN, an updated value of an updated hidden state of the one or more hidden states as a first activation function applied to a first function, the first function comprising one or more weight matrices, and 
 adjusting the weights of the nodes of the RNN to minimize a loss function subject to a set of monotonicity constraints, wherein the set of monotonicity constraints causes output risk indicators computed by the RNN and the input predictor variables input into the RNN to have the monotonic relationship, and wherein adjusting the weights comprising adjusting weight values in the one or more weight matrices; and 
 
 causing the output risk indicator to be transmitted to a second computing system for controlling, based on the output risk indicator, access by the target entity to one or more interactive computing environments. 
 
     
     
       16. The non-transitory computer-readable medium of  claim 15 , wherein the first function comprise (i) a first weight matrix multiplied by the input predictor variable and (ii) a second weight matrix multiplied by a stored value of a hidden state of the one or more hidden states,
 wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints comprises:
 adjusting first weight values in the first weight matrix, wherein the first weight matrix is nonnegative, and 
 adjusting second weight values in the second weight matrix, wherein the second weight matrix is nonnegative. 
 
 
     
     
       17. The non-transitory computer-readable medium of  claim 16 , the operations further comprising:
 computing, by the RNN, the output risk indicator, as a second activation function applied to a second function, the second function comprising a third weight matrix multiplied by the updated value of the hidden state, 
 wherein adjusting the weights of the nodes of the RNN subject to the set of monotonicity constraints further comprises adjusting third weight values in the third weight matrix, wherein the third weight matrix is nonnegative. 
 
     
     
       18. The non-transitory computer-readable medium of  claim 17 , wherein:
 the first activation function has a respective derivative that is always nonnegative; and 
 the second activation function has a second respective derivative that is always nonnegative. 
 
     
     
       19. The non-transitory computer-readable medium of  claim 18 , wherein:
 the RNN is a long short-term memory (LSTM) network; 
 the first activation function has a respective range that is strictly nonnegative; and 
 
       the second activation function has a second respective range that is strictly nonnegative.